Question: $\dfrac{9}{2} \div \dfrac{2}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{2}{9}$ is $\dfrac{9}{2}$. Therefore: $ \dfrac{9}{2} \div \dfrac{2}{9} = \dfrac{9}{2} \times \dfrac{9}{2} $ $ \phantom{\dfrac{9}{2} \times \dfrac{9}{2}} = \dfrac{9 \times 9}{2 \times 2} $ $ \phantom{\dfrac{9}{2} \times \dfrac{9}{2}} = \dfrac{81}{4} $